On the other hand, it is generally believed that the astrophysical black holes are not in an empty space but instead surrounded by an extremely luminous accretion flow which definitely affects the obtained image of the black hole. There are many papers and interesting discussions, show how the presence of accretion material modifies the black hole shadow. In 1978, Luminet extends the Synge’s work to a more realistic case in which the Schwarzschild black hole is surrounded by an accretion flow [1]}. He studied the light deflection of a black hole surrounded by a geometrically thin, optically thick accretion disk and showed that the optical appearance of the black hole and the photon ring depend on both the location and profile of the accretion flow. In an interesting viewpoint, Gralla et al. by studying the rings around black hole shadow of M87* showed that depending on the intersection points of light rays with the plane of the disk there exist different rings called direct emission, lensing ring and photon ring. In this model, the accretion flow around the black hole is optically and geometrically thin [2]}. Moreover, the shadow of the Schwarzschild black hole surrounded by a geometrically thick, optically thin accretion flow has been studied by Cunha et al. in [3]}. A simple spherical model of optically thin accretion in the space-time of the Schwarzschild black hole, and the study of properties of its shadow have been done in [4]}. Narayan et al. argue that the behavior of the black hole image in spherical model is different from geometrically thin disk model regarding that the inner edge of the disk can leave an remarkable imprint on the image, especially when the edge of disk is out of the photon orbit. The shadow of quintessence Schwarzschild black hole surrounded by accretion flow for two types of the accretion flow, optically and geometrically thin disk accretion flow, and also spherically accretion flow, is studied in [5]}. Authors have studied the effects of quintessence state parameter and accretion flow on the optical appearance of black hole [5]}. Also, authors have studied the similar behavior for 4-dimensional Gauss-Bonnet black holes and explored the influence of both the Gauss-Bonnet parameter and spherical accretion flow on the properties of the black hole shadow [7]}. The optical appearance of black holes in the context of Rastall gravity with different spherical accretions has been also studied in Ref. [8]}. For further studies about the effect of the location and profile of accretion flow which surrounded the black hole space-times in alternative gravity theories see, [9]}–[10]}.
